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GeoGebra

Proofs Practice

Author:C Morrell, Tim Brzezinski
In Geometry, we're never allowed to assume anything--we need to prove it using logic and reason. Slide the sliders on the diagram below, and try and answer the questions that follow to the best of your ability. Interact with this applet below for a few minutes, then answer the questions that follow. As you do, feel free to move the BIG WHITE POINTS anywhere you'd like on the screen!

Q1:

What did you notice when you slid the black bar at the bottom? How did the sides and angles compare in both triangles?

Q2:

Are the triangles exactly the same? Are there any sides or angles that are not exact? How do you know?

Q3:

To be considered congruent, you need to prove that some corresponding pieces in the triangles are exactly the same. How many corresponding sides and/or angles could you say are congruent based on the markings? Do you think that's enough to prove that the triangles are the same?

Q4

Below are 4 reasons we use to prove triangles congruent in Geometry. Which one do you think makes sense based on the markings in this diagram? Angle-Angle-Side (AAS) Side-Angle-Side (SAS) Side-Side-Side (SSS) Angle-Side-Angle (ASA)

Q5:

Below are 4 reasons we use to prove triangles congruent in Geometry. Which one do you think makes sense based on the markings in this diagram? Angle-Angle-Side (AAS) Side-Angle-Side (SAS) Side-Side-Side (SSS) Angle-Side-Angle (ASA)

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